Convergence of the empirical spectral distribution function of Beta matrices

Convergence of the empirical spectral distribution function of Beta matrices

Let Bn=Sn(Sn+αnTN)−1, where Sn and TN are two independent sample covariance matrices with dimension p and sample sizes n and N, respectively. This is the so-called Beta matrix. In this paper, we focus on the limiting spectral distribution function and the central limit theorem of linear spectral sta...

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Bibliographic Details
Main Authors: Bai, Zhidong, Hu, Jiang, Pan, Guangming, Zhou, Wang
Other Authors: School of Physical and Mathematical Sciences
Format: Article
Language:English
Published: 2015
Subjects:
Beta matrices
CLT
LSD
Multivariate statistical analysis
Online Access:https://hdl.handle.net/10356/80954
http://hdl.handle.net/10220/38995
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Institution: Nanyang Technological University
Language: English
Description
Summary:Let Bn=Sn(Sn+αnTN)−1, where Sn and TN are two independent sample covariance matrices with dimension p and sample sizes n and N, respectively. This is the so-called Beta matrix. In this paper, we focus on the limiting spectral distribution function and the central limit theorem of linear spectral statistics of Bn. Especially, we do not require Sn or TN to be invertible. Namely, we can deal with the case where p>max{n,N} and p<n+N. Therefore, our results cover many important applications which cannot be simply deduced from the corresponding results for multivariate F matrices.

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